Question

Can you please help me with this assignment?  

You are a Correctional Officer in the Secured Housing Unit (SHU) at the state prison. Warden Lind has recently come under scrutiny for possible biased practices at the prison. Investigators from the governor’s office are investigating the allegations and they have decided to interview inmates from the SHU. The problem is that the warden has treated gang members and minority prisoners very badly in the past. Currently there are 121 inmates in the SHU. Of these inmates, 61 are minorities, 34 are gang members and 89 are violent offenders. The investigators will randomly draw inmates’ names from the SHU to interview.

Q₁: What is the probability of selecting a minority inmate for the interview?

Q₂: What is the probability of selecting a gang member for the interview?  

Q₃: What is the probability of selecting a non-minority inmate for the interview?  

Q₄: What is the probability of selecting a non-violent inmate for the interview?  

Q₅: Based on your probability analysis, should Warden Lind be concerned?  

Answer 1

1) The probability of selecting a minority inmate for the interview =

No. of minority inmates / total inmates = 61/121

2) The probability of selecting a gang member inmate for the interview =

No. of minority inmates / total inmates = 34/121

3) The probability of selecting a non-minority inmate for the interview =

No. of non-minority inmates / total inmates = (121 - 61)/121 = 60/121

4) The probability of selecting a non violent inmate for the interview =

No. of non violent inmates / total inmates = (121 - 89) /121 = 32/121

5) Warden Lind will be concerned if either a minority inmate or a gang member inmate are asked to interview, as they have been treated badly by him and are more likely to speak out against him.

Now, inmates can be 2 or even 3 of 3 things at the same time, eg: any inmate can be a minority AND a gang member inmate.

So we don't know the exact number of inmates who are both minority and gang members. But what we do know is the number of violent inmates = 89.

As we've seen,

The probability of selecting a non violent inmate (gang member or minority inmate) for the interview = 32/121, which is relatively less.

Therefore, he should not be that concerned as the chances of picking up a non violent inmate are low.

Cheers!